Stretch normal/displacement to give entire mesh one color
After hours of messing around, I finally found a way of doing this. If you stumble across this post seeking the same results, here's how I did it:

Firstly, I re-orientated the normals of each face of the sphere to point upwards.
Next, I disabled shadows for the material seen in the image above. This can be done in the material settings.
Lastly, I created another translucent material that, with the help of a shader to RGB and color ramp node, will only ever be black or white. I assigned this material to the bottom half of the sphere.


I'm satisfied with the result. The cons is that this method will work best with eevee, only work with spheres/simple objects and the top half of the sphere won't cast any shadows.
You can also get something similar by combining a translucent and diffuse shader with the add shader node. This might be better in some circumstances.
I hope this post helps someone ^^